For this case we must find the solutions of the following equation:
[tex]4x ^ 2-x + 9 = 0[/tex]
We apply the cudratic formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 4\\b = -1\\c = 9[/tex]
Substituting:
[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (4) (9)}} {2 (4)}\\x = \frac {1 \pm \sqrt {1-144}} {8}\\x = \frac {1 \pm \sqrt {-143}} {8}[/tex]
Thus, the complex roots are:
[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]
Answer:
[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]
